Chapter 4 Individual and Market Demand
Chapter 4 Individual and Market Demand ECO 420K
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This 4 page Class Notes was uploaded by Natalie Strawn on Saturday June 11, 2016. The Class Notes belongs to ECO 420K at 1 MDSS-SGSLM-Langley AFB Advanced Education in General Dentistry 12 Months taught by John Thompson in Summer 2016. Since its upload, it has received 19 views. For similar materials see MICROECONOMIC THEORY in Economcs at 1 MDSS-SGSLM-Langley AFB Advanced Education in General Dentistry 12 Months.
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Date Created: 06/11/16
June 7, 2016 Microtheory Chapter 4 - Individual and Market Demand The Lagrangian Method Use the method of Lagrange multipliers to maximize (or minimize) a function subject to a constraint. Step 1: State the problem Ø = U(X,Y) - ʎ(PxX +PyY – I) Note: PxX + PyY – I = 0 Step 2: Differentiating the Lagrangian 1) ∂ Ø/ ∂X = MUx ʎPx = 0 2) ∂ Ø/ ∂Y = MUy ʎPy = 0 3) ∂ Ø /∂ʎ = I – PxX -PyY = 0 -These “first order conditions” (FOCs) have to be satisfied in order to maximize the objective function subject to the constraint. Step 3: 1) MUx/Px =ʎ 2) MUy/Py = ʎ 3) PxX + PyY = I Interpret the FOCs: -(1) and (2) give us the equal marginal principle -(3) says the consumer has to be spending all her income Ex. Px is $8, Py is $40, and income (I) is $200. Utility: U(X,Y) = 4(X^(1/2))(Y^(1/2)) BC: 8X + 40Y =200 Step 1: State the problem Ø = 4x^(1/2)y^(1/2) - ʎ(8x + 40y – 200) Step 2: Differentiate 1) ∂ Ø/ ∂X = 2x^(1/2)y^(1/2) ʎ8 = 0 2) ∂ Ø/ ∂Y = 2x^(1/2)y^(1/2) ʎ40 = 0 3) ∂ Ø /∂ʎ = 200 -8x – 40y = 0 Step 3: Plug in 5y = x so, 8x + 40y = 200y =2.5 U = 4(12.5^(1/2))(2.5^(1/2)) = 22.36 Individual demand -Changes in price cause changes in consumption. (Figure 4.1) -From this, we can derive individual demand. -The price consumption curve (PPC) shows utility maximizing combinations of two goods as the price of one changes. -Note: Food and clothing are substitutes and complements along the PCC in (Figure 4.1) -Changes in income cause changes in consumption -causing the demand curve to shifts -The income consumption curve (ICC) shows utility maximizing combinations of two goods as income changes. -The ICC may bend backward in the case of an inferior good. (Figure 4.3) -An Engel curve shows the relationship between income and quantity consumed for some good. (Figure 4.4 and 4.5) (Table 4.1) Suppose Px falls; two things happen a) X becomes cheaper relative to Y (and vice versa) b) Real income increases The substitution effect (a) is the tendency to want to buy more of the relatively cheaper good, and less of the relatively more expensive good. The income effect in (b) is the tendency to want to buy more of both goods (assume both are normal) These occur simultaneously when prices change, but we can isolate them (graphically or mathematically) Income and Substitution effects -Suppose clothing and food fall (figure 4.6)? -A Giffen good is a special case of a good with an upward sloping demand curve… …comes from the income effect of a strongly inferior good. -suppose clothing and food, and Pf falls (food is a Giffen good) (figure 4.7) The Slutsky Equation decomposes the total change in X: dX/dPx = ∂ x/∂ p – (∂x/∂I) Note: (X|U=U*) First term on the RHS is the sub effect 2ndterm is the income effect Market Demand is the horizontal summation of individual consumers’ demands. (figure 4.8) -suppose ten identical consumers with inverse demand: P = 4 – 2Q -solve for direct demand to sum horizontally: Q = 2 – 0.5P Qm = Q1 + Q2 + … + Q10 = 10(2-0.5P) Qm = 20 – 5P (direct) P = 4 – 0.2Qm (inverse) -A special case is the isoelastic demand curve, with the same elasticity everywhere. Examples: Qd = kP^-r Qd = 1/P In such a form, -r is the elasticity. (figure 4.11) -constant expenditure, unit elastic -Welfare economics is the analysis of how various policies affect different groups’ well-being. -Consumer surplus measures the difference between what a consumer was willing to pay (buyer value) and what they had to pay (price). (figure 4.13) (figure 4.14) -Consumer surplus is like “profit” to the consumers from buying some quantity Q* at some price P*. Ex: Qd= 600 – 20P Calculate change in CS and change in expenditures when change in price is $12 to $10. CS1 = (18 X 360)/2 = 3240 CS2 = (20 X 400)/2 = 4000 Change in CS = + 760 Total expenditure: Change in expenditure = -720 + 400 = -320
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